A GRADUATED SCALE FOR 
DETERMINING MENTAL AGE 



C. B. CORNELL, PH. D. 

ACTING HEAD OF THE DEPARTMENT OF PSYCHOLOGY 
UNIVERSITY OF KENTUCKY. LEXINGTON 



'iHi 

ssaaoNOD jo Aawaan 



'A Graduated Scale for Determining Mental Age' 



Clare Brown Cornell 



A Thesis 



Presented to the Faculty of The Graduate College in the 

University of Nebraska in Partial Fulfillment of 

Requirements for the Degree of Doctor 

of Philosophy 



Department of Philosophy 

Lincoln, Nebraska 

1915 



l\^\2 



'j:i 



i^ 



l^'c^ 



Publishers 

STATE JOURNAL CO. 

Frankfort, Ky. 



Copyright 1918 by 
Clare Brown Cornell 



0. Of £) 



Acknowledgments. 

In working out a problem which has as its basic material 
the measuring of human intelligence one is quickly brought to 
feel his absolute dependence on his fellows. In art, in the other 
fields of science, in literature, given a well equipped laboratory, 
or a shelf of carefully selected books and periodicals, the task 
of working out an investigation becomes one of cataloging and 
classifying known facts and of establishing new ones. But in 
the field of psychology the investigator is peculiarly helpless 
unless he can secure the intelligent co-operation of people who 
see the value of his work. The author of this monograph was 
especially fortunate in this respect, and wishes to take this op- 
portunity of expressing his appreciation of the assistance given 
him by the teaching force of the Lincoln (Nebr.) Public Schools. 
Thanks are particularly due to Superintendent Fred M. Hunter, 
who gave him the freedom of the entire system ; and to the prin- 
cipals of the eight schools from which the children were selected, 
namely, E. Kuth Pyrtle, principal of McKinley School, Lena 
Merrill, principal of Saratoge School, Emma Morrill, principal 
of Everett School, Mattie Allen, principal of Whittier School, 
J. Belle Corbin, principal of Bancroft School, Clare MePhee, 
principal of Capitol School, Bertha K. Green, principal of 
Clinton School, and Sadie Baird, principal of Elliott School. 

The author is gi-eatly indebted to Dr. H. K. Wolfe, head of 
the Bepartment of Psychology in the University of Nebraska, 
who suggested and directed the investigation, and to Dr. Wini- 
fred Hyde for helpful criticisms during the process of arrang- 
ing the material. 

The Author. 
Lincoln, Nebr., July 20, 191.5. 



After carefully checking the data and after using the scale 
in a large number of cases covering a period of three years, the 
author feels justified in presenting the work in its complete 
form. The results obtained by the use of the scale are accurate 
to a marked degree. Correlation of the individual tests with 
results obtained by the Binet scale are decidedly close. 

C. B. C. 
Lexington, Ky.. July 10, 1918. 




A Graduated Scale For Determining 
Mental Age. 

Introduction. 

[HE science of mental measurement is a logical out- 
growth of experimental psychology and can be 
traced indirectly to Pechner and Wiindt. Al- 
though based upon seemingly intangible psychic 
phenomena, its methods nevertheless parallel 
those of the other sciences. There is this 
difference, however, between the two fields: 
in the other sciences definite units of measurement have 
been established and generally accepted, whereas in the science 
of mental measurement, very few standard imits have as yet 
been fully developed, owing to the peculiar difiQculties inherent 
in any attempt to determine the required norms. "The problem 
for (Quantitative study of the mental sciences is to devise means 
of measuring things, differences, changes and relationships for 
which standard units of amount are often not at hand, which 
are variable, and so unexpressible in any case by a single figure, 
and which are so complex, that to represent any one of them a 
long statement in terms of different sorts of quantities is com- 
monly needed. "<25'^> But in spite of the difficulties encountered 
a relative degree of success has attended the search for units 
whereby mental abilities can be relatively measured. 

Methods of procedure have been evolved by Pechner/'> 
Wundt,<32) Ebbinghaus,"> Muller,<i7) and others, but the appli- 
cation to pedagogical problems has been a comparatively recent 
development. Undoubtedly the greatest stimulus toward this 
came from Binet in France, whose work was quickly taken up 
in Germany and in this country. The various modifications and 
elaborations of Binet 's tests have filled the field with a rich 
literature. 

The current interest in mental tests is undoubtedly largely 
due to the need felt, on the part of teachers and supervisors, 
for an efficient instrument wherewith correctly to diagnose and 
cla.ssify school children. This attitude is wholly in keeping with 
the recent trend of our public school system which is more and 
more readjusting itself to the problem of meeting the needs of 
the individual child. 

The following investigation is the result of an attempt by 
the author to find a satisfactory scale for mental measurement 



6 A Graduated Scale for Determiniog Mental Age 

to be used in the public schools. In casting about for standard- 
ized tests none was found which combined the age scale with 
the essentials of diagnosis. 

The novice iu the work is at once attracted by the Binet- 
Simou scale, but it is to be doubted if the results obtained in its 
application can be considered reliable. A careful analysis of 
the scale, from the standpoint of the psycho-elinicist, reveals 
many defects which cannot be explained away. The scale falls 
far short of being the magical instrument which its many ex- 
ponents claim it to be and will never serve as an instrument of 
exact analysis. However, a criticism of the Binet scale is beyond 
the scope of the present work, especially iu the light of the 
literature of the subject.* Its relative success in clinical work 
would seem to result from the fact that, throughout the scale, 
there exists a psychological framework which insures approxi- 
mate results despite a large amount of extraneous material. 

The greatest obstacle encountered in the practical applica- 
tion of any method is the lack of coherence and system. In the 
measuring of mental processes the tests must necessarily cover 
a wide range in order to determine the true ability of the subject. 
Tests which ascertain ability in one phase must be supplemented 
by tests applicable to other operations of the mind. Take, for 
example the Ebbinghaus "Combinationsmethode, '" familiarly 
known as the completion method. (8.40i),(29.2S3) j^ ^\^^ ^ggt a 
story is given to the child with syllables or entire words omitted 
fi'om the text. The problem is for the child to fill in the blank 
spaces in an intelligent manner in the least po.ssible time. The 
author claims that this is a "real test of intelligence, a simple, 
easily applied device for testing those intellectual activities that 
ai*e fundamentally important and significant both in the school 
and in life." Actual application, however, shows that the test is 
not as comprehensive as the author claims, is difficult to evalu- 
ate, ^^^^ and is dependent on school training.*^") But, in spite of 
these objections, it may be used as one of a group owing to its 
close correlation with intelligence. '^'^^e) 

The scale proposed in the present monograph is an attempt 
to combine the determination of mental age with psychological 
diagnosis. It is composed of nine separate tests, divided into 
three general group , as follows : 

A. Perception, tests I. and IX. 

B. Memory. 

(a) Auditory, tests II. and III. 

(b) Visual, test IV. 

(c) Logical, test V. 

C. Judgment. 

(a) Visual proportion, test VI. 

(b) Constructive problems, test VII. 
(e) Definitions, test VIII. 

The characteristic features of the scale are as follows: (1) 
The same tests are used for all ages and the mental age deter- 
mined by the manner of the individual reaction, measured in 

*For criticisms of the Binet scale see especially references 7, 22, 
23, 24, 27 and 35. 



A Graduated ycale for Determining Mental Age 7 

terms of the relative number of points for each age. (Norms have 
been established for the ages six to fourteen, inclusive.) This 
method dispenses with a great amount of unnecessary labor, 
both on the part of the experimenter and of the child, becaxise 
of the fact that standing is measured in terms of ability to 
react. (2) The tests chosen are necessarily of such a nature 
as to appeal to the interest of the child regardless of age. More- 
over, as a proof that they are genetic tests of intelligence, the 
ability to react to each test increases uniformly as we go up 
the age scale, with a fairly wide I'ange between the upper and 
lower limits. (3) The tests measure native ability regardless 
of training. This feature opens up a wide field for discussion. 
For example, Binet uses as tests, counting, knowledge of money, 
family name, dates, and others which may be influenced by 
training. One of my tests is for the child to name all the objects 
that he can think of during one minute, with the eyes closed. 
This may be open to criticism of training, but the evidence shows 
that the more intelligent the child, the greater the number of 
associations, even though the type of words suggest the influ- 
ence of previous training or environment. (4) The tests are 
comprehensive, that is, they are so arranged that the several 
basic mental operations may be analyzed. (5) They are compact 
and systematic. The apparatus, aside from the stop-watch, can 
be made in the school room or ofSce, and, with the exception of 
the card of objects, may be carried in a large envelope. The 
number of tests is small but each is important. (6) The tests 
may* be easily and quickly applied. It is believed that any 
teacher who understands the principles of psychological method 
can, after perhaps fifty trials, conduct the test in about thirty 
minutes, with comparatively accurate results. (7) The results 
may be accurately evaluated, provided the data are correct. 
This is made possible by the systematic scoring by means of 
points.* (8) The results are significant from the standpoint of 
the clinical psychologist, indicating to the trained observer the 
type of the subject. 

It is believed that the scale is a simple and coherent system 
which may be efficiently used, both to determine mental age and 
mental type. In the hands of the novice it will indicate not only 
the group to which the child belongs, but also his predominating 
characteristics. The expert will find it valuable as an index to 
further tests which may be deemed necessary for a more com- 
plete analysis of the subject's mentality. In any case, with 
careful manipulation, the mental age will be closely determined. 

Source of the Data. 

In establishing the norms presented in this work the tests 
were given personally by the author to about 550 children of 
the Lincoln Public Schools. Of this number, 75 were tested be- 
fore the method was fully worked out, about 75 more were tested 



*The entire plan of the work was completed and the data more 
than half collected before the method of the point scale used by 
Yerkes and Bridges (34) was available. Reference to their scale will 
show the radically different methods between the two systems. 



8 A Graduated Scale for Determining Mental Age 

during the year for clinical purposes, leaving 404 in the group 
from which the scale was ultimately established, or an average 
of 45 for each of the nine ages. These children were taken from 
eight different schools, collectively representative of all classes 
of population usually found in a cosmopolitan city. MeKinley 
School is located in the heart of the business section with a de- 
cidedly cosmopolitan community furnishing the students, with 
a predominance of foreign shopkeepers and peddlers. Saratoga 
School, in the south part of the city, has grown up withiu five 
years to accommodate the children of a multitude of small home 
owners. Everett School is one of the oldest in the system, with 
a very stable student population, in a fairly well-to-do commun- 
ity. Whittier School is located on the north side in a much 
poorer section of the city than those previously mentioned, with 
a large German element and many mechanics. Bancroft has the 
same class of children in attendance as Whittier. In both of these 
schools the absence of fourteen-year-olds in the upper grades 
was noticeable. Capitol School is located in the oldest residence 
section with many children of comparatively rich parents in at- 
tendance. Clinton School is an opposite extreme, being located 
in an outlying district of cheaper homes and rented houses. The 
last school visited, Elliott, is located in an average residence sec- 
tion and has a stable attendance. 

The children were selected by the principal in conjunction 
with the teacher, after the problem had been carefully explained 
by the experimenter. Teachers and principals, as well as the 
children, were intensely interested in the work and put forth 
every effort to contribute to its success. It was required of each 
child that he be "just average or normal," neither accelerated 
nor retarded, that is, that the pedagogical age should corrsepond 
with the chronological age. The child's physical development 
and condition at the time of taking the test were carefully con- 
sidered. A great deal of confidence is placed in the type of 
children selected because of the fact that each principal has 
known practically each child from the time of entrance, in most 
cases being entirely familiar with the child's family history. 
Piirthermore the work was undertaken at an opportune time, 
because of the fact that the Principals' Club was working on 
the problem of classification, and the principals were particular- 
ly interested in the method of procedure. 

The collection of data was begun in November, 1914, and 
was continued until the middle of June, 1915. 

The children of each age group were within the limits of 
five months over and four months under the year; for example, 
the seven year group ranged from six years and eight months 
to seven years and five months, with an average fairly close to 
the year. An effort was made to keep the mean variation of age 
as low as possible. 



























13 




14 





A Graduated Scale for Determining Mental Age 9 

TABLE I. 

Age Average Age Mean Variatioa 

Yrs. Mo. Da. Mo. Da. 

1—6 2 — 15 

— 20 2—3 

— 16 2—3 

0—2 2-11 

— 15 2—3 

0—7 2 — 13 

0—5 2 — 16 

— 19 2 — 12 

— 19 2—6 

Method of Conducting Tests. 

The method employed in conducting the tests is similar to 
that used in the Binet tests and their modifications. A room was 
provided in each building which would be as quiet and free from 
disturbance as possible. In a few cases where it was necessary 
to use the principal's office the tests were suspended during the 
transaction of routine business. In each school the experimenter 
was given every possible consideration which contributed not a 
little toward the successful manipulation of the tests. A small 
table was placed opposite the windows with the experimenter 
seated facing the light and with the child on his right. Prom 
the moment the child entered the room he was treated with 
cordial respect and made to feel perfectly at ease, with the un- 
derstanding that he was contributing toward the solution of the 
probkm rather than merely being tested. In some cases the 
problem was explained in some detail, while in others the child 
was merely informed that his help was desired in finding out 
the difference between the upper and lower grades. In no case 
was the test begun until the child felt at home and was in the 
attitude which would produce uniform results. In the great ma- 
jority of eases the children entered the room with an evident feel- 
ing of pleasant anticipation and curiosity due, perhaps, to the 
advertising which the tests had received at the hands of those 
previously taking them. Each child was cautioned not to tell 
anything about the teste and no evidence was discovered which 
would indicate that they had been talked over among the chil- 
dren. As a matter of fact the nature of the tests is such that 
previous information or coaching would have but little effect on 
the final results. The tests were all given during the regular 
school hours and averaged thirty minutes for each child. All 
data was recorded on the accompanying blank. Drawings made 
by the child were kept on a separate sheet of blank paper 
which was later attached to the blank. The recording was 
done by the experimenter and no effort was made to conceal this 
fact from the subject. 



A Graduated Scale for Determining Mental Age 



TEST BLANK 



Name School Date 

Grade Born 

Mental Age Age — 

I. Card of objects (5 seconds) Bu. Co. Cr. Gla. Ky. Kni. Mbl. Na. 

Ni. Pn. Pel. Pi. Scl. Scr. St. 

II. Repeating digits _ _ ' 

III. Repeating syllables 

IV. Learning figures, 1 2 3 Total 

V. Association words (One Minute). 

VI. Height of man standing by 50-foot tree. (Over) feet. 

VII. Problems (1) Square (2) Rhombus (3) Rectangle 

(4) Paper cut (5) Clock, 9:00 2:00 (6) Reconstruct 

triangles (7) Paper cut 

VIII. Definitions. 

(1) Fork. 

(2) Horse. 

(3) Automobile. 

(4) Poet. 

(5) Tree. 

(6) Kindness. 

(7) Sweetness. 
(S) Charity. 
(9) Justice. 

(10) Worm and snake. 

IX. Sorting cards min sec piles 



Equivalent value min.... sec. 



Test I. 



In this test fifteen objects, familiar to all children, are 
fastened on a white card board 37 em. square, and covered with 
another card board of the same dimensions (See Fig. 1.) The 
objects are in description and size as follows: One black button 
29mm. in diameter; an aluminum comb 130mm. long; a green 
crayon of standard form and size ; a pair of blue glasses ; a flat 
Yale key; a pearl-handled penknife 60mm. long; a blue 
marble 14mm. in diameter; an eight-penny nail; a Buffalo 
nickel; a gold pen point; a red paper pencil 80mm. long; a 
red clay soap-bubble pipe ; a small pair of scissors ; an ordinary 
screw 60mm. long; and a five-cent postage stamp. 

In giving the test the covered card is placed in front of 
the child and used as a stimulus for close attention with the ex- 
planation: "/ have a lot of things fastened on this card; now 
I'm going to show them to you for just a few seconds and then 
when I cover them up you tell me what you saw. Now, look 
closely, ready — ." The objects are exposed for five seconds and 
must be covered quickly but quietly. Any undue disturbance 
on the part of the observer is sufficient in some eases to inter- 
fere materially with the reaction. Incidentally, it is necessary 
to keep the child's interest and attention focussed on the work 
from beginning to end of the series. This is usually accom- 
plished by presenting the tests in succession without pause. 

The results are summarized in table II. 










noYS 








;iRL.s 






BOTH 






Ago 


No. 


Tolal 


Av. 


.M. V. 


No. 


T.>lj| 


Av. 


M. V 


N... 


Tolal 


Av. 


y. V 


6 


20 


67 


3.3 


.65 


20 


65 


3.3 


.57 


40 


132 


3.3 


.61 


7 


23 


97 


4.2 


63 


17 


71 


4.2 


.80 


40 


168 


4.2 


.70 


8 


19 


82 


4.3 


■.83 


22 


96 


4.4 


.85 


41 


178 


4.3 


.84 


9 


27 


135 


5.0 


.89 


26 


123 


4.7 


.85 


53 


258 


4.9 


.8S 


10 


20 


100 


5.0 


.90 


22 


111 


5.0 


1.05 


42 


211 


5.0 


.98 


11 


24 


13S 


5.8 


.90 


25 


141 


5.6 


1.10 


49 


279 


5.7 


1.01 


12 


22 


12:; 


5.6 


1.11 


18 


106 


5.9 


.70 


40 


229 


5^7 


.;ifi 


13 


25 


146 


5.9 


.99 


21 


133 


6.3 


.85 


46 


279 


6.1 


.92 


14 


2S 


153 


6.1 


1.12 


2S 


1S4 


6.6 


1.26 


53 


337 


6.4 


1.21 



'I'lic iiuTeasi.' (if tli(> ivfra^e muulii'i' nt' olijeL-ts remembered 
for eiieli ;i^e is g-i\cii in Kiyure 2, which also represents the 
mean variation of the children of each age from their own 
average, in the lower graph. The curve shows that the varia- 
bility of children in handling this test inerea.ses materially 
from six to fourteen vears. 



Table I IT. is a comparison - 
ind six-year-old childi-eii in abilit\ 



-old 
iects. 































..^iid 


;^ 










^ 


^^- 


Vt' 








^ 


h^-' 










/ 








- ' 


V -^. 


/ 




-^y 




r 


--- 


7^ 


^ 


I 


■^ 


y-' 































11 24 

12 22 

13 25 



TABLE 

I.; ^•I•s, 



TABLE 
Boys. 



TABLE V. 
Girls 



\1 


5 


B 


4 


5 


12 


Vi 


7 


1 


9 


6 


10 


« 


5 


3 




f) 


1(1 


5 


11 


:; 


11 


4 


12 


14 


H 


5 


12 


• 


15 


74 


t;7 


•jt; 


Hf, 


■.\:\ 


'M 



A Graduated Scale for Determining Mental Age 



13 



■ A comparison of the totals of the above tables indicates 
the following sex differences: The girls mention the button, 
crayon, glasses, pencil and scissors, a significant number of times 
more than do the boys; the boys mention the key, knife, nail, 
nickel, and screw oftener than the girls; they rank about the 
same in the case of the comb, marble, pen, pipe and stamp. This 
comparison, while somewhat irrelevant, is significant to the 
psychologist, and is represented graphically in figure 3. 





BuCaCf 


&/. 


/iy. 


Kti MlxNa.Ni 


Pn 


Pd.RiSci.&r 


St 


70 






H 








Soys 

G,W5 










1 1 














60 








^_ 








































r- 


















— 












r*a 


1 








h-1 


"" 
















-- 




1 




'Ol.. 




















1 




1 




^ 


•HI 

30 












... 




























1 1 


-*• 




._, 























1 1 




















v: 










.-J 








L. 














i: 
















































.. 














— 








































J 

























Test n. 

The second test is one used by Binet and viniversally 
•adopted by those who have made modifications of the Binet- 
Simon scale, namely, auditory memory for digits. For conveni- 
ence the child is requested to look at a designated object which 
will turn him sidewise, with the right side to the experimenter. 
This method was found more convenient than to have the child 
turn completely around and moreover gives the experimenter 
an opportunity to discover whether the subject is of the motor 
type by watching the movement of the lips while giving the 
syllables. The only explanation given is "^ay these numbers 
after me." The following digits are then read in a smooth, even, 
distinct voice, without accent except for a natural lowering of 
the voice on the last digit of each group, which becomes the 
signal for the child to begin repeating. The rate is slightly faster 
than one digit per second. 



A Graduated Scale for Determining' Mental Age 



847 


4297 


52814 


384296 


1695847 


41629385 


315 


5318 


47395 


279314 


2964375 


25718394 


926 


6194 


58319 


618492 


9285164 


58261947 



The child is required to repeat correctly two out of any 
given group in order to receive credit for that group. In other 
words, he is given credit for the number of digits in the 
highest group in which he is able to repeat correctly two num- 
bers. For example, in the fours he may repeat 4-2-9-7 correctly, 
fail in repeating 5-3-1-8, and then repeat 6-1-9-4 correctly, 
when he will proceed to the next higher group. Then in the 
fives, if he should make one correct repetition, but fail in the 
other two, his credit is for four digits only. 

Table VI. contains the results of this test with the number 
of digits repeated correctly and the mean variation for each 
age. 













1 


FABLE 


VI. 






















Repeating 


Digits. 


















BOYS 






GIRLS 










BOTH 




Ape 


No. 


Toul 


Ay. 


M. V. 


No. 


Total 


Av. 


M. V. 


No. 


Total 


Av 


M.V. 


6 


20 


S7 


4.3 


.54 


20 


90 


4.5 


.70 


40 


177 


4.4 


.64 


7 


23 


116 


5.0 


.52 


17 


82 


4.9 


.60 


40 


198 


4.9 


.56 


8 


19 


102 


5.4 


.81 


22 


124 


5.6 


.78 


53 


226 


5.5 


.80 




27 


l.'>4 


5.7 


.58 




146 


5.6 


.81 


53 


300 


5.7 


.70 




20 


113 


5.7 


.47 


22 


121 


5.5 


.73 


42 


234 


5.6 


.62 




24 


139 


5.8 


.53 


25 


146 


5.8 


.61 


49 


2S5 


5.8 


.57 




22 


133 


6.0 


.50 


IS 


106 


60 


.33 


40 


239 


6.0 


.43 




25 


154 


6.1 


.44 


21 


127 


6.0 


.43 


46 


281 


6.1 


.44 




25 


160 


6.4 


.74 


28 


177 


6.3 


.68 


53 


337 


6.4 


.70 



^^ 


^'^ 


1^ ^ 


v^^'^<;''«i. >^ 


^^,^S^^/ 


■' 





5 /O 

Fig. 4. 



// IZ /3 14- 



It will be noticed here that the increase is greatest from 
six to eight, with a slight drop at ten, and a constant increase 
from ten to fourteen. The per cent, of increase in toto from 
six to fourteen is given in table VII. The increase in ability to 
repeat digits is shown graphically in figure 4, the lower curve 
showing the variability of the mean variation, which is greatest 
at eight and lowest at twelve and thirteen. 



A Graduated Scale for Determining Mental Age 





TABLE VII. 




Boys 

Girls 

Both 


6 Yrs. 14 Yrs. 

4.3 6.4 

4.5 6.3 

4.4 6.4 


% Increase. 
49 
40 
46 



Test III. 

The third test is also taken from Binet and, like the pre- 
ceding one, is a test of auditory memory. It consists in re- 
peating syllables in sentence form, beginning with a word of 
two syllables, with each succeeding sentence or group of words 
greater than the preceding by two syllables. The sentences used 
are Goddard's modification of those given by Binet and Simon 
and are taken from Wliipple's Manual. ^^*> 

1. Papa. 

2. Slipper. Letter. 

3. It is cold and snowing. 

4. I have a dog. He's a fine one. 

5. His name is Jack. Oh, what a naughty boy. 

6. It is raining out doors, but we can stay inside. 

7. We are having a fine time. We found a mouse in a 
trap. 

8. Let's all go for a walk today. Give me that big hat 
to wear. 

9. Poor Helen has just torn her new dress. She will 
surely feel sorry for that. 

10. Why should anyone want to do injury to such beau- 
tiful creatures as birds? 

11. We expect to have a great time at the seashore, digging 
in the white beach sand all day long. 

12. When the train crosses the road the engineer will see 
the wagon standing beside the apple tree. 

13. My young brother Frank had a fine time on his vaca- 
tion this simimer. He went fishing almost every day. 

14. To start a fire in the open is one of those tricks which 
evei-yone thinks he can perform until he tries it. 

15. He sinks the net in the water and waits until he can 
see the fish distinctly, lying perfectly still and within 
reach. 

16. The first rapid was only the beginning; half a mile 
below we could see the river disappear between two 
points of rock. 

17. One day the children's grandmother came to visit 
them and the children were very happy because she 
told them beautiful fairy stories. 

18. The Indians used to perform many kinds of queer, 
horrible dances, in the course of which they yelled and 
shrieked as if suffering the most painful torture. 

It is necessary to pronounce the words distinctly, at a 
uniform rate, and without undue accent. The main objection to 
this test is the lack of uniform increase in difficulty from one 
sentence to the next. For example, I found, as did Mrs. Squire^^^ 
and others, that the children could often repeat the twelfth 



16 A Graduated Scale for Determining Mental Age 

sentence correctly after having failed in the two or three pre- 
ceding sentences. Hence, after my preliminary tests, I changed 
the sentence from "When the train crosses the road the engineer 
will hloiv the whistle and the fireman will ring the hell," to 
"When the train crosses the road the engineer will see the wagon 
standing beside the apple tree," a sentence less rich in associa- 
tive connections. 

Tliis test is given under the same conditions as the second 
and should follow it without a break with the simple state- 
ment, "Repeat these words." It will be noticed that the general 
method of procedure in this and the preceding test differs from 
that given by Binet in that the child's maximum ability is 
found at once, that is, without interposing other tests and then 
reverting to the memory tests, if ability of a higher age is shown. 

In order to receive credit for a sentence it is considered 
necessary for the child to repeat every syllable correctly. But if 
a slight error occurs in one sentence, and the child can repeat the 
next correctly, he is given credit for the latter. I made one con- 
cession in regard to verbatim repetition in the eleventh sentence. 
Here I accepted as correct "fine time at the seashore," whereas 
the sentence reads "great time at the seashore." This mistake 
occurred so frequently in the preliminaries in the cases of chil- 
dren who could repeat the two succeeding sentences that I felt 
justified in making the change. 

In no ease is the child informed of his errors; when the 
maximum has been reached we pass immediately to the next test 
as if there were no more sentences to be given. In this, as in 
all the other tests, the average child will watch for confirma- 
tion of his work. It is, of course, necessary for the experimenter 
to be perfectly passive, and give no sign of commendation prior 
to the completion of the work in hand. 

At an early stage in the woi-k I discovered that considera- 
ble time could be saved by beginning with the fourth sentence 
for the lower ages and with the seventh or eighth for the upper 
ages. 

TABLE Vlll. 
Summary of Test III. Ability to Repeat Syllables. 

BOYS GIRLS BOTH 

Age No. Total Av. M. V. No. Total Av. M. V. No. Total Av. M. V. 

6 20 310 15.5 1.4 20 318 15.9 .77 40 628 15.7 1.08 

7 23 374 16.3 1.1 17 268 15.8 1.08 40 642 16.0 1.09 

8 19 322 16.9 1.5 22 378 17.2 1.55 41 700 17.1 1.53 

9 27 492 18.2 1.75 26 470 18.0 1.46 53 962 18.1 1.60 

10 20 354 17.7 1.73 22 404 18.4 1.75 42 75S 18.0 1.74 

11 24 492 20.5 2.25 25 471 18.8 1.76 49 963 19.7 2.00 

12 22 448 20.4 2.19 18 363 20.2 2.10 40 811 20.3 2.15 

13 25 582 23.4 2.97 21 448 21.3 2.14 46 1030 22.4 2.60 

14 25 610 24.4 2.91 28 662 23.6 3.05 53 1272 24.0 2.99 

The increase in ability to repeat syllables, according to this 
data, is fairly uniform, with a close parallelism between the two 
sexes. The greatest increase is between the ages of twelve and 
thirteen, with a slight drop between nine and ten. My results 
agree with those of Binet showing twenty-four syllables for 



A Graduated Scale for Determining Mental Age 17 

the fourteen year group while the Binet tests use twenty-six for 
the fifteen year group. 





Zk 

'•1 


































; 


-y! 


















^ 


f 


~y 












. 


^ 






// 




> 




^ 


^ 






^ 


/ 


/ 




t 


14 








^ 


-^■ 










1 


^. 


f^ 


^ 














lO 


— ^ 



















a 9 10 II 

Fig. 6. 



The comparative ability of the fourteen and six year group 
is given in table IX. 



Boys 
Girls 
Both . 



6Yrs. 
15.5 
15.9 
15.7 



14 Yrs. 
24.4 
23.6 
24.0 



Increase. 
57 
48 
53 



Curves for variation in ability to repeat syllables, and mean 
variation for the different ages are given in figures 5. 



18 A Graduated Scale for Determiuiug Mental Age 

Test IV. 

Immediately following the third test the 

Tuhild is given a test involving visual and motor 
memory. The material used is five odd shaped 
figures which have been adopted from those given 
in Seashore's Manual/^^-i^^' By referring to 
ligure 6 it will be noticed that these are made 
u]> of a vertical and a horizontal line, each thir- 
^^i^HM teen mm. in length, and drawn at right angles to 
I one another. At the opposite, or unattached end 

I of the vertical line, a third line, six and one-half 

V I mm. in length, is drawn, at an angle of 45°. The 

^ variation in form of the figures is made by differ- 

ent combinations of these three lines. The first 
^g^^,^^ and la-st, the second and fourth, may be said to 
I be pairs, in that they are identical but inverted. 
I This similarity was noticed bj' some children and 
^1 became an aid in memorizing the figures. 
\| The method is as follows : The child is given 

a piece of blank paper and shown the figures for 
perhaps a second while the operator makes this 
explanation : "Now I'm going to let you look at 
these things for just a few seconds, and, then 
/I when I take them away, you draw as many as 

I you can rememher. Here's the pencil." The fig- 

I ures are removed at the word "seconds." This 

tiii^MiiBw places the child in the proper attitude and shows 
definitely wliat is wanted in the briefest possible 
amount of time. I hit upon this method after 
several experiments in the preliminaries, during 
^k wliieh I used the word "figures." I found that 

I this suggested the arabic figures, hence I adopted 

I the word "things" while letting the child see the 

«bbJL^b ob.ieets themselves. Following the above explana- 
p. g tion, after a pause of about two seconds to notice 

by the child's expression whether or not the 
problem was clear, the slip on which the figures were drawn is 
placed on the blank paper directly in front of the child with 
the remark: "Now study them carefully." After an exposure 
of ten seconds the slip is quietly but quickly removed and the 
child told to draw as many as he can remember. During this 
process the operator must be absolutely quiet. A slight dis- 
turbance may interfere with the reaction, but in general, the 
child draws at once all of the figures which he remembers. I 
found that it was useless to wait for further results after about 
fifty seconds. When the child has drawn as many figures as 
possible from the first exposure his paper is turned over or 
covered up for another trial, with the remark "Draw here next 
time," which indicates that the experiment is to be repeatec", 
and also inhibits the tendency to look at the previous work. 
The test is given three times with the same instructions in each 
instance. The child is not permitted to look at his work until 



A Graduated Scale for Detei'mining Mental Age 19 

the three trials are tinished and no hint should be given con- 
cerning his accuracy until the completion of the test. 

, In evaluating this test I allow one point for each figure 
correctly drawn, giving full credit for repetition of figures 
drawn in succeeding trials, but not for figures duplicated in the 
same trial. Half credit is given if a figure is reversed, but no 
credit if a figure is inverted. 

After a little practice the operator is able to count the 
number of correct figures while the child is drawing them, im- 
mediately filling in the blank. The data for each trial were 
kept separate, but in the following table, which gives the sum- 
mary, the total for the three trials is used. 















TABLE 


X. 
















Summary of Test IV., 


Visuo-motor Memory. 










BOYS 








GIRLS 






BOTH 




Agt 


No. 


Total 


Av. 


M. V. 


No. 


Total 




Av. 


M. V. 


No. 


Total 


Av. 


M. V. 


6 


20 


41.0 


2.0 


1.3 


20 


31.5 




1.6 


.96 


40 


72.5 


1.8 


1.12 


7 


23 


64.0 


2.8 


1.43 


17 


38.5 




2.3 


1.19 


40 


192.5 


2.6 


1.28 


8 


19 


67.0 


3.5 


1.21 




67.0 




31 


1.55 


41 


134.0 


3.3 


1.4 


9 


27 


125.5 




1.56 


26 


87.5 




3.0 


1.40 


53 


213.0 


4.0 


1.54 


10 


20 


86.5 


4.3 


1.54 


22 


100.0 




4.5 


1.82 


42 


185.5 


4.4 


1.69 


11 


24 


138.0 


5.7 


2.36 


25 


123.5 




4.9 


1.47 


49 


261.5 


5.3 


1.84 


12 


22 


129.0 


5.9 


1.82 


18 


93.5 




5.2 


1.66 


40 


222.5 


5.6 


1.82 


13 


25 


171.5 


6.8 


1.83 


21 


142.0 




6.7 


1.71 


46 


313.5 


6.8 


1.80 


14 


25 


203.0 


8.1 


1.62 


28 


195.0 




7.0 


1.7 


53 


398.0 


7.5 


1.86 



This proved to be one of the most interesting and valuable 
of .♦he entire series of tests. The method of drawing the figures, 
the motions with the pencil which often accompany the learn- 
ing, and other facts which arise in individual cases, make the 
test of especial use in diagnosis, aside from its value as a unit 
in the present work. For example, a student who is a distinct 
motor type will trace tiie figures in the air while studying them. 
Mature students who are proficient in hand work will draw with 
accuracy and precision regardless of their ability in other linc^ 
of work. Moreover, the correlation with intelligence is very 
close, the curve being strikingly parallel with the summation 
curve shown in figure 18. 

The norms show a typical increase in ascending the age 
scale, with a comparatively small mean variation. See figure 
7. This test fully meets the important requirements of an in- 
telligence test, being uniform throughout, and having a wide 
range between the upper and lower limits, as shown in table XI. 



6 Yrs. 14 Yrs. % Increase. 
Boys 2.0 8.1 300 

Girls 1.6 7.0 338 

Both 1.8 7.5 317 



A Graduated Scale for Determining Mental Age 




Test V. 

Niimher of Objects Named in One Minute. 

This test is adapted from the third test in Binet's twelve 
year series, in which the child is required to name as many 
words as he can in three minutes. My instructions to the child 
are as follows: "Shvt your eyes. Now name over all the things 
you can think of; just any thing — any object." This is usually 
sufficient except in a minority of cases in the lower years. If 
the child does not understand he will say so, perhaps opening his 
eyes, in asking for further information. In such a case it may be 
necessary to explain what is meant by thing; ordinarily the 
statement "A book is a thing" is sufficient to start the reaction. 
The child will shut his eyes and begin with the word book. I 
snap the watch at the sound of the first word, allowing the re- 
action to continue for one minute. If the key-word — book — is 
required, it is not counted in the total number of words. Credit 
is given for the common nouns only. If the child gets started 
on a series of proper names it is necessary to interrupt with the 
expression, "No, not that kind, just common things." This 
occurs, however, vei\v seldom. The most interesting case of the 
kind was noticed during the preliminary trials. A very pre- 
cocious girl of ten years started to name the states and was 
well down the list before sidetracked. Occasionally, in the lower 
ages, the child will need additional stimulus. During longer 
pauses suggestive of waning attention, I break in with "Some- 
thing else," which serves to renew the effort. 

For purposes of diagnosis the words should be taken down, 
but I found it impracticable to do so except for the younger 
children. From the psychological standpoint this test is inter- 
esting and very significant in its bearing on mental ability. 
"Besides the number of words, one can note their relations; 
some subjects give only detached words, each of which requires 
an effort to recall. Others give a series of words, the 
furnishings of a school, various articles of clothing, etc. Some 



A Grraduated Scale for Determining- Mental Age 21 

u^e only names of common objects, others cite abstract qual- 
ities or rather far-fetched words. All this gives an idea of the 
mentality of the subject. "<'''^' A series given by a child of six 
maj- contain words which have no obvious relation; as, for ex- 
ample, the following: pencil, garden, doll, boat, horse, chair. 
On the other hand a mature child names objects in a regular 
series of associated words, often without a break. The following 
list was given by a boy of ten : book, school, tires, building, 
house, sidewalk, street, ground, street car, trolley, iron, black- 
smith shop, cigars, candy, confectionery, paper, pencil, music, 
music rack, piano, flute, book, magnifying glass, orange, potato, 
radish, beet, carrot, turnip, hygiene. Rapidity of naming ob- 
jects is, of course, facilitated by association, hence the older 
child will give a greater number of words. "Little children ex- 
haust an idea in naming it; thej- saj', for example, hat, then 
pass on to another object without noticing that hats differ in 
color, in form, have various parts, have dift'ei-ent uses and acces- 
sories. . . . Their lack of skill in the use of language, and in 
the analysis of ideas, is very striking. "^''■^^^ 

It is evident that there is a close correlation between general 
intelligence and ability to enumerate objects. It is also evident 
that this ability increases with the growth of richness in as- 
sociation until the age of twelve when the maximum seems to 
have been reached. Hence, for the present purpose, the results 
arg evaluated by merely counting the number of things named 
— ^the number of common nouns — leaving the analysis of the 
train of associated words for application in diagnosing the in- 
dividual case. 

It is believed that the method here presented is superior 
to that used by Biuet. for three reasons: (1) By having the 
e.yes closed the material is to a great extent introspective. The 
child may begin by naming the objects which he has just seen on 
the table, but quickly switches to the schoolroom, the home, or 
the playground. (2) By allowing one minute instead of three 
time is saved and the child is not fatigued. The number of 
words in the first twenty seconds is usually greater than that of 
the last forty, and no advantage can be gained by prolonging 
the time. (3) The instructions are given in a manner which 
causes the child to name nouns — ideas — rather than words. 

In the majority of cases I was assured of a maximum of 
effort on the part of the children. This can be noticed by the 
facial expression, which can be carefully studied while the eyes 
are closed for this exercise. 

TABLE XII. 
Number of things named in one minute. 



6 


Ko. 

20 


268 


13.4 


5.3 


20 


235 


11.7 


3.95 


40 


503 


12.5 


4.65 


7 


23 


327 


14.2 


4.2 


17 


239 


14.1 


5.02 


40 


566 


14.2 


4.57 


8 


19 


350 


18.4 


4.6 


22 


380 


17.3 


4.82 


41 


730 


17.8 


4.69 




27 


624 


23.1 


5.36 


26 


554 


21.3 


4.70 


53 


1178 


22.2 


5.36 


10 


20 


453 


22.6 


6.05 


22 


485 


22.0 


6.40 


42 


938 


22.3 


6.22 


11 


24 


704 


29.3 


6.56 


25 


639 


25.6 


4.97 


49 


1343 


27.4 


5.82 


12 


22 


661 


30.0 


4.55 


18 


628 


34.9 


6.37 


40 


1289 


32.2 


6.45 


13 


25 


775 


31.0 




21 


606 


29.0 


9.19 


46 


1381 


30.0 


7.72 


14 


25 


776 


31.0 


5^64 


28 


924 


33.0 


6.36 


53 


1700 


32.1 


5.85 



22 



A Graduated Scale for Determining Mental Age 



The curve indicating increase in number of things named 
is given in figiire 8. The increase is greatest between the ages 
seven and nine, ten and twelve. No gain is made from twelve 
to fourteen. The drop between twelve and thirteen is caused by 
a lessened ability on the part of the girls, which can perhaps 
be traced to physiological causes. The boys outrank the girls 
in all ages except at twelve and fourteen. 

The lower curve of figure 8 shows the fluctuation of the 
mean variation. This curve is strikingly similar to the curve 
of increase in ability (the upper), except that the variations 
are one year later. For example, at ten years the mean variation 
is high, while the increase in ability over the preceding year is 
but slight; at eleven the mean variation drops, while the ability 
curve rises; at thirteen the mean variation is high, with a cor- 
responding drop in ability; at fourteen the conditions are just 
the reverse. 

The per cent, of gain of the fourteen year old children over 
the six year old children in number of ideas named during one 
minute is given in table XIII. 



TABLE XII 

6Yrs. 

Boys 13.4 

Girls 11.7 

Both -2.5 



14 Yrs. 
31.0 
33.0 
32.1 



134 
182 
157 




Test VI. 

The sixth test is a problem involving judgment of visual 
proportion. The child is told to draw a picture of a tree which 
is fifty feet high, with a man standing by it. For ages six and 
seven this was varied, because of the fact that the term fifty 
feet possesses but little significance for younger children. In 
fact, it was doubted at first whether this would be a test ap- 



A Graduated Scale for Determining Mental Age 23 

plieable to all ages, but subsequent trials proved it to be 
especially valuable. The children of six and seven years of age 
were told to draw "A great, big, high tree, fifty feet high with 
a man standing by it."* 

The height of the tree and man were measured in milli- 
meters and the comparative height of the latter computed at 
once on the slide rule by means of the following simple formula : 
11=50 M/T, where H represents the required height of the man, 
M actual height of man in millimeters, and T actual height of 
tree in millimeters. In practice I measure M, divide by 2, 
mentally, then on the slide rule divide this by T, properly plac- 
ing the decimal. 

While the children, with a few exceptions, had taken the 
regular course in drawing, the sense of proportion does not dis- 
play itself, except relatively, until the later years are reached. 
A consistent effort to draw to scale is not shown except during 
the years thirteen and fourteen, and then only in scattered in- 
stances. In general, the crudest drawings are accompanied by 
the poorest sense of proportion. "We have exemplified here the 
development of the ability of self expression through drawing. 
The children of six make the customary rectangular trunk with 
a spray of branches protuding from the upper end. The lack 
of co-ordination of the accessory muscles is shown by the square 
head and body of the man. Training in drawing displays itself 
in the style of tree (for example, during the holiday season the 
children all drew Christmas trees), but there is no evidence of 
transfer to ability to judge proportion. 

The relative height of the man with variations is given in 
table XIV. 

TABLE XIV. 
Man and Tree 



6 20 389.0 19.4 5.33 20 443.6 22.1 6.29 40 S32.6 20.8 5.86 

7 23 441.3 19.2 5.18 17 415.5 24.4 7.83 40 S56.8 20.4 7.30 

8 19 397.0 20.9 6.80 22 255.8 1G.2 4.11 41 752.8 18.4 6.00 

9 27 430.8 15.9 4.80 26 535.9 20.6 7.66 53 966.7 18.2 6.83 

10 20 328.5 16.4 6.29 22 453.8 20.6 7.67 42 782.3 18.6 7.32 

11 24 365.7 15.2 5.80 25 346.3 13.7 4.31 49 712.0 14.5 4.70 

12 22 214.4 9.8 3.52 18 304.5 16.9 8.17 40 518.9 12.9 6.56 

13 25 302.3 12.1 4.46 21 293.0 14.0 7.52 46 595.3 12.9 5.90 

14 25 290.5 11.6 3.92 28 331.4 11.8 4.80 53 621.9 11.7 4.36 

The comparative height of the man for the different ages 
is indicated in the upper graph in figure 9. The irregularity 
is to be expected from six to nine. The ten year group shows 
a weakness in the sense of proportion while a marked gain is 
shown from ten to twelve. There is no improvement from 
twelve to thirteen, but a decided advance from thirteen to four- 
teen. The boys indicate a higher ability in this problem than 
the girls; furthermore the points of greatest increase for the 

*A11 drawings made by the child are kept on the sheet of blank 
paper furnished him in test IV. 



24 A Graduated Scale for Determining Mental Age 

boys are coincident with a backward drop for the girls, for 
example, ages nine, ten and twelve. 




The curve of mean variation and that indicating relative 
height of the man, are strikingly similar. The two curves for 
girls are virtually parallel. Likewise the cui-ves for boys, and 
the ciirves for the entire group. This signifies that the groups 
which show greatest ability in judging the proportionate height 
of the man are the least variable. 

While the curve is more irregular than one would hope 
for, nevertheless the test has great value in diagnosis. The 
intellectual child, the mature child, never fails to grasp the 
significance of the test. On the other hand, young children and 
the immature in the upper ages neglect the main point to a 
great extent. In clinical cases I have had a precocious ten year 
old girl draw the man six feet in height ; while a badly retarded 
girl of fifteen drew the man twenty-two feet in height. 



Test VII. 

Problems. 

This test is in reality a group of seven problems, designed 
to test the judgment, ingenuity, and inventive ability of the 
child. 

Problem 1. — A square piece of cardboard, 72mm. in each 
dimension, is cut into four equal isosceles triangles along the 
two diagonals. The material used in this and the two succeed- 
ing problems is a high grade four-ply card, black on one side, 
gray on the other. The child is required to keep the black side 
up. The child is given the four triangles and requested to put 
them together so that they will look like the model (a card board 
of the original size and form). The instructions are, "Put these 
together so that they will look exactly like that," spoken while 
placing the pieces in front of the child. 



A Graduated Scale for Determining Mental Age 




In problems 1, 2 and 3, the time required for the solution 
was taken with the stop watch and a record kept. It was soon 
found that ability was not directly proportional to the time 
reqiiired and, after a large number of preliminary tests, the 
problem was counted correct if solved within three minutes. 
The precocious child is apt to put the pieces together quickly, 
but a child who slowly and deliberately, after repeated trials, 
finally reaches a solution should receive full credit. 

Problem 2. — A rhombus, whose sides were each 72mm., 
angles 60° and 120°, was cut into four equal right triangles 
along the two diagonals. A model of the same dimensions was 
used. The entire procedure was as in problem 1, allowing three 
minutes for a solution. 

These two problems are similar in form yet present contrast- 
ing difficulties. In the first, the child immediately places two 
triangles together, hypotenuse against hypotenuse, forming a 
square. This is repeated with the other two triangles and the 
wliole put together in the form of a rectangle. The child of low 
mentality usually is satisfied with this rectanglar form and is 
ready for the next test. The normal child, on the other hand, 
breaiis up the form and tries another method. The procedure in 
problem two is to form a symmetrical figure by placing two tri- 
angles together along their longest side. As a matter of fact, 
the aesthetic demand for symmetry and balance asserts itself 
in all ages in these three tests, and must be overcome before a 
solution is possible. For example, the children, after picking up 
two triangles, will habitually put them together, thus 




26 A Graduated Scale for Determiniug Mental Age 

Problem 3.* — A rectangle 52min. x 80 mm. is cut into 
tliree triangles, all similar but unequal, as indicated in figure 
10. The method is the same as that used in the two preced- 
ing problems. 

In case of failure, we pass to the next test with the re- 
mark, "We'll let that one go for a few minutes. Here's an- 
other one which I think is easier." In no case should the atten- 
tion of the child be drawn to a lack of success. The effort seemed 
to be constant, and usuallj^ represented the maximum of the 
child's ability. In several instances, after finishing these three 
tests, I have had a child say, "Yes, hut I want to try that other 
one again. I believe I can get it noiv." 

The general results for these problems are given in the fol- 
lowing table : 









TABLE XV. 












Problem 1 


Problem 2 


Problem 3 






No. 


Ave. Time 


No. 


Ave. Time 


No. 


Ave. Tin 


Age 


No. Ch. 


Correct 


in Sect 


Correct 


in Sec. 


Correct 


in Sec. 




40 


8 


46 


11 


60 


2 


75 


7 


40 


9 


63 


14 


81 


7 


60 


8 


41 


17 


74 


15 


75 


13 


48 




53 


14 


66 


23 


81 


23 


74 


10 


42 


20 


66 


23 


60 


23 


69 


11 


49 


26 


67 


37 


65 


35 


56 


12 


40 


20 


59 


30 


55 


23 


73 


13 


46 


28 


72 


36 


70 


37 


70 


14 


53 


36 


76 


45 


59 


37 


86 



Table XVI. gives the percentages of correct solutions of 
each problem for each age. 

TABLE XVI. 

Boys Girls Both 

% Solving % Solving % Solving 

Age 123 123 123 

6 30 35 5 5 20 5 18 27 5 

7 33 61 26 12 18 6 25 43 18 
S 47 47 37 41 27 18 44 37 27 
9 30 41 56 35 46 31 32 44 44 

10 55 60 60 50 64 64 53 62 62 

11 58 79 67 48 72 72 53 76 70 

12 55 87 60 50 72 61 53 80 35 

13 76 84 84 57 76 76 68 80 80 

14 92 80 80 93 90 64 93 85 72 
This table bears me out in the method used in evaluating 

the results of these three problems. Indicated graphically in 
figure 11, we may infer that the length of time is more or less 
irrelevant, provided three minutes is the limit. 

*Taken from Mrs. Squire's monograph (22). 

tAve. T. is the average time of those who actually solved the 
problems. While somewhat irrelevant, I give this table to show that, 
of those who can put the puzzles together within the time limit, there 
is no correlation with age. In fact, we may say that the average time 
of those who can put the puzzles together within three minutes, in- 
creases with age. I suggest this explanation: The younger children 
either solve it at once or reach their limit of ingenuity after. the first 
few trials, while the older children are more persistent, a larger pro- 
portion solving the puzzle, but with a longer average time. 



A Graduated Scale for Determining' Mental Age 27 





















■« 


V / 






^ 








/. 


5 70 


/\ 


/' 


V 


-V 


^T" 


^ 


/ 


^s 


'"' 


/ 


\ 


/ 






\^ 




a-" 


















i; 






Prahiam J 

t 

3 





























Problem 4. — This is the paper cutting test used by Binet in 
his 1908 series. A sheet of note book paper is twice folded double 
in the presence of the child, and the corner formed by the 
center of the paper is cut off, forming a diamond shaped figure 
in the center. The child is required to draw a picture of the 
paper showing the cut. The instructions are given in the follow- 
ing sentence: "I fold this paper over like this, then like this, 
then I take the scissors and cut off that corner. Now draw a 
picture of the paper just as it would look if we were to open it and 
spread it flat on the table." The cut must be drawn approxi- 
mately at an angle of forty-five degi-ees with the edges to pass 
as correct. That is, a square in the centre of the paper with its 
sides parallel with those of the paper, is classified as a failure. 





TABLE XVII. 






First Test i 


n Paper Cutting. 






Boys 


Girls 


Both 


Age 


% 


% 


% 















22 


6 


15 




31 


31 


31 




48 


39 


43 




55 


55 


55 






68 


72 




73 


84 


78 




76 


81 


78 


14 


88 


93 


91 



Problem 5. — The Binet-Simon clock problem, slightly modi- 
fied, was used as the fifth in this group. The problem is to tell 
what time it would be by the clock if the hands were inter- 
changed when it is (a) nine o'clock; (b) two o'clock. The in- 
structions to the child are as follows: "Suppose it is nine o'clock 
by the watch and I change the hands, putting the big one where 
the little one is, and the little one where the big one is. What 
time would it be?" This was repeated for the second part using 
the words two o'clock. Full credit is given if both are answered 
correctly, half credit if one is answered correctly. 



A Graduated Scale for Determining Mental Age 





TABLE X 


VIII. 




Interchanging of Hands of Clock at 9 


and 2. 




Boys 


Girls 


Both 


Age 


% 


% 


% 


G . 











7 











8 


18 


14 


16 


9 


43 


23 


33 


]0 


55 


59 


57 


n 


91 


68 


74 


12 


89 


86 


88 


13 


94 


88 


91 


14 


96 


97 


96 



Problem 6. — This is the reversed triangle used by Binet in 
the adult series. The child is shown two equal right triangles 
so placed that they will form a rectangle. The problem is to 
draw the two triangles as they would appear with the lower one 
so turned that line A-B would be against line C-D, with angle 




B joining angle D. (P"'ig. 12.) The triangles are cut from a 
card board rectangle 82mm. x 52 mm. No letters or marks are 
allowed on the triangle. In giving the exercise the triangles 
are placed on the table before the child with the explanation: 
"Imagine the lower triangle to he teemed around so that this 
edge (indicating A-B), is placed against this edge (indicating 
C-D), and this angle (B), against this angle (D). Draw a 
picture of the two triangles in that position." If the child does 
not comprehend, the instructions are repeated. Credit is allowed 
only when the angles are properly placed. The common error 
in this problem is to place the right angle in the middle of line 
C-D, rather than at point D. 





TABLE XIX. 






Rearranging Two Triangles. 




Age 
6 


Boys Girls 

% % 



Both 



7 
8 
9 
10 
11 
12 
13 
14 



5 5 

10 5 
8 
13 17 
32 5 
28 32 


15 
20 
30 



A Graduated Scale for Determiuing- Mental Age 29 

Problem 7. — This problem is also taken from Binet, being 
an adult test in the 1905 series. While giving the explanation 
the experimenter folds a rectangular sheet of note paper, as in 
problem four; the cut is triangular, made in the side which 
presents a single fold. The subject is not permitted to touch 
the paper and must not fold another sheet. Binet says of this 




pi-oblem: "This test is difficult. Most subjects simplify the 
solution greatly. They think that only one hole is cut, a square 
or a diamond, sometimes a five-pointed star, and that position is 
in the center of the paper." <^'^^' To be correct two diamonds 
must be drawn in line with each other on the longest diameter, 
one in the upper, the other in the lower half. If the diamonds 
are drawn on the shorter diameter, half credit is allowed. 

TABLE XX. 

Second Paper Cut. 

Boys Girls Both 

Age % % % 

6 

7 

8 2 1 

9 11 2 7 

10 10 18 14 

11 40 36 38 

12 43 50 46 

13 44 66 54 

14 60 70 65 

The seven problems given in test VII. are grouped together 
in the final scale and treated as one, hence I classify them in 
table XXI. in the same manner as each of the preceding tests. 

It may be mentioned that experience soon teaches an ex- 
perimenter that it is useless to give all the tests in this group 
to each child. Only the first four are given to the six and seven 
year group. Problem five cannot be given to a child who is un- 
able to tell time. Problem six is seldom given to a child who 
is apparently running below twelve in mentality. If a child 
shows signs of precocity he is given each one of the group. The 
rule which I observed throiighout was to give the test if there 
was the least possibility of the child's passing it. 



A Graduated Scale for Determiuiug Mental Age 













TABLE 


XXI. 
















S 


ummary of the 


Seven Tests 


in Group 


VII. 










BOYS 






GIRLS 






BOTH 




Afi-: 


No. 


Toul 


Av. 


M. V. 


No. 


Total 


Av. 


M. V. 


No. 


Total 


Av. 


M. V 


6 


20 


14 


.7 


.56 


20 


6 


.3 


.48 


40 


20 


.5 


.6 


7 


23 


33 


1.43 


.84 


17 


7 


.4 


.56 


40 


40 


1.0 




S 


19 


35.5 


1.87 


1.03 


22 


30.5 


1.4 


1.10 


41 


66 


1.61 


1.08 


9 


27 


61.5 


2.28 


1.18 


26 


45.5 


1.8 


1.21 


53 


107 


2.02 


1.21 


10 


20 


61.0 


3.05 


.92 


22 


69.0 


3.14 


1.10 


42 


130 


3.10 


.97 


n 


24 


94.5 


3.94 


1.31 


25 


93.0 


3.7 


.97 


49 


187.5 


3 82 


1,09 




22 


90.0 


4.09 


1.03 


18 


75.5 


4.2 


.74 


40 


165.5 


4.14 


.89 


i;i 


25 


122.5 


4.90 


1.00 


21 


94.5 


4.5 


.76 


46 


217.0 


4.72 


1.00 


14 


25 


131.0 


5.21 


1.17 


28 


150.5 


5.4 


.87 


53 


218.5 


5.31 


.87 



See lower curve Pig. 14 for the norm. 

































/■ 














^ 


r 










f 


ff' 












/ 










X 


-;?; 


^^ 












>^ 
















^ 


'' < 


J s 


A 


J / 


1 1 


Z 1 


S' 14 



Test Vin. 

Definitions. 

It is generallj- agreed that ability to express ideas verbally is 
a good criterion of intelligence. In the search for a test which 
could be used throughout the age series and at the same time 
parallel the genetic development of the child, no better test could 
be found than a .series of definitions. The words selected fall 
into three groups, as follows: (1) Terms used in the every day 
life of the child, fork, horse and automoiile; (2) Terms which 
are not so easily classified and which require a higher type of 
definition than is usually given in the first group, poet and tree; 
(3) Abstract terms, kindness, sweetness, charity and justice. A 
tenth was added under this heading, namely, the difference be- 
tween a worm, and a snake. 

The test is given with the following instructions : "/ am go- 
ing to ask you several questions. Answer them the very best 
you can. First, what is a fork?" 

The answers for the present purpose, are easily classified 
in three groups : 

1. Simple repetition or silence. The common response for 
a six-year-old is "Why, a fork is a fork." "A horse is a horse." 
Children of this type use the same response for fork, horse, 



A Graduated Scale for Determining Mental Age 31 

automobile and tree and, as one would expect, make no response 
to the other questions, except the last "What is the difference 
betiven a worm and a snake"?" the answer, "A snake's bigger," 

2. Definitions in terms of use. — A few typical examples : 
^4. fork is a thing to eat with. A horse is to ride on, or to pull 
carriages. An automobile is to ride in or carry groceries in. A 
tree is to get fruit off of. As Binet says, ' ' All these answers are 
clearly infantile, not only in their incorrect form, but also in 
their conciseness, and finally in the state of mind which they 
reveal ; scarcely any children of seven years are exclusively 
utilitarian in their definitions. "^^'^^^ 

3. Definitions in terms superior to use. — When an attempt 
is made to give a more elaborate definition the answers at once 
become much more diversified. The first step is to give the class, 
next the differentia. The type of answer is in large measure 
dependent upon the degree of the child's familiarity with the 
object being defined. The lowest class in this type is that in 
which the genus is given followed by the use. The real value 
of the definition depends, of course, upon the number of dif- 
ferentia given, and the classification. In this group horse is 
defined as, an animal; a beast of burden; a domestic animal 
used as a beast of burden. 

Method of Evaluating. — At first glance the problem of 
evaluating this series of definitions, so that it may be used in a 
point system, may seem especially difficult. But the scale which 
was adopted permits an accurate evaluation after a little prac- 
tice. It is, briefly, this : For each definition, allow one point if 
in t*^rms of use only. If the proper class is given allow one 
point. For each differentium allow one point. With the one 
restriction — no definition shall receive more than three points. 
In the tenth, the difference between a worm and a snake, allow 
one-half point for each valid difference. 

1. Pork. — To eat with, score 1. Utensil used to eat with, 
score 2. A table utensil used in eating, score 3. 

2. Horse. — To ride, score 1. Animal to ride on, score 2. 
Domestic animal, score 2. Four-legged animal, score 1. Domestic 
animal used for hauling wagons, score 3. 

3. Automobile. — To ride in, score 1. A vehicle, score 1. 
A vehicle to ride in, score 2. A four-wheeled vehicle, score 1. 
A thing run bij machinery, score 1. A ivagon run by an engine, 
or a self-propelled vehicle, score 3. 

4. Poet. — Man that writes poetry, score 1. (In general 
tautological definitions do not receive credit. The above, how- 
ever, involves a higher meaning than to say "A poet is a poet.") 
Man who writes verses, score 2. Ma7i who writes stories that 
rhyme, score 3. Man that writes beautiful thoughts in verse 
form, score 3. 

5. Tree. — A thing to climb, score 1. Used for lumber, 
score 1. To get fruit off of, score 1. A plant, score 1. The largest 
of all plants, score 2. A big piece of wood growing in the ground, 
score 2. A large plant, with big trunk and branches, used for 
wood, score 3. 

6. Kindness. — To be kind, no credit. Being nice, score 1. 



32 



A Graduated Scale for Determining Mental Age 



Helping others, score 2. To be polite, unselfish and helpful to 
others, score 3. 

7. Sweetness. — To he sweet, no credit. Something that 
tastes like sugar, score 2. A taste, score 1. Like kindness, score 
1. There are two kinds; something that tastes like sugar and 
tvhen people look sweet and are nice to one another, score 3. 
(Note — Perhaps kindness and sweetness should have been re- 
versed. As it is, the idea of sweetness being like kindness, is given 
oftener than was anticipated.) 

8. Charity. — Helping others, score 2. Giving help to the 
poor, score 3. (When this word was defined at all the answers 
were similar to those given. In the main, the concept was con- 
crete rather than abstract.) 

9. Justice. — To be just, no credit. To do right, score 2. 
To do unto others as you would have them do to you, score 3. 
// a person is in jail and gets what's coming to him, that's 
justice, score 2. 

10. Difference between a worm and a snake. — One-half 
point for each difference. Size, form, teeth, skin, head, motion, 
bones, feet, color, are typical differences mentioned. 

In evaluating the above definitions one must not be de- 
ceived by a high sounding phrase, but must measure the ideas 
contained in the phrase. For example, children occasionally 
respond to, "What is a fork?" with, "A fork is an instrument 
used to convey food to the mouth." This does not necessarily 
indicate a higher degree of intelligence; it is more likely a re- 
sult of training. 



Summary of 


TABLE XXII. 
Points Made In Definition 


Test. 




Boy, 


Girls 




Both 


Age Av. M. V. 


Av. M. V. 


Av. 


M.V. 


6 3. 1.75 


3.4 l.S 


3.20 


1.86 


7 4.4 1.48 


4.15 1.36 


4.29 


1.45 


8 6.3 1.76 


4.95 1.05 


5.58 


1.49 


9 7.4 1.50 


6.13 1.66 


6.75 


1.64 


10 7.1 1.90 


8.32 2.58 


7.70 


2.52 


11 11.8 2.17 


10.62 1.80 


11.17 


2.02 


12 13.25 2.98 


11.36 2.14 


12.40 


2.80 


13 14.12 2.57 


13.48 2.52 


13.82 


2.56 


14 15.3 3.86 


15.40 2.91 


15.35 


3.16 

















\/ 












<. 


-y- 












,'/ 


^^' 














/ 












--y 


^ 








/ 




^ 


'y 


// 


s* 


y^ 


:> 


^ 


< 


'-^ 


i*-4 


^'^ 



























6 9 10 II 12 'i 14- 
Pig. 16. 



A Graduated Scale for Determining Mental Age 



33 



Test IX. 

Sorting Cards. 

For this test a set of fifty cards is employed utilizing the 
rather complex function of discrimination of form and color. 
The cards used are of highest grade duplex calling card stock, 
in size the same as an ordinai-y playing card, 63x89mm. Spots 
are arranged as shown in figure 16, forming five sets of ten 
cards each. Colors used are blue, green and red; forms are 
circle, lOVo mm. in diameter, a square 9 mm. each side, and an 
equilateral triangle each of whose sides is 14 mm. (Area of 
spots practically equal.) The cards are sized with collodion as 
a protection to the colors. 

In all sets the colors are retained in the same order, namely, 
blue at the top, green in the middle, and red at the bottom.* 





After carefully shuffling the cards they are shown to the 
student with the explanation, "Now I want you to sort these 
cards for me. I'll show you "the different kinds there are. This 
one, and this one, etc. Novj you are to sort them over, putting 
ilie ones that are just alike in the same piles. Do you see how they • 
are all different?" In the meantime the experimenter may be 
shuffling the cards allowing sufficient time — about one minute — 
for the child to discover the fundamental differences in the five 
sets. Then gathering up the five sample cards, place them 



•Sets may be secured by communicating with the author. 



34 A Graduated Scale for Determiuing Mental Age 

at the bottom of the deck and hand all to the child with the re- 
mark: "If you find a card and have no place to put it, start a 
new pile. Just as quickly as you can now, hut don't make any 
mistakes." A record is kept of the time in minutes and sec- 
onds, with the number of errors. 

In this test care should be taken to see that the child under- 
stands the problem thoroughly. The differences in the cards 
should not be explained, but, in the cases of slower children, a 
little longer time may be allowed in looking at the cards at 
first. The common type of error is to place the two sets which 
have circles at the top in the same pile. Cards must not be in- 
verted. 

As a means of quickly detecting mistakes in piling, the set 
number — 1, 2, 3, 4, or 5 — is placed on the back in the upper 
left hand corner. An error is counted each time a new number 
appears in the course of running them through. That is. sup- 
pose set 4 cheeks as follows: 4-4-4-3-4-2-2-2-4-2. We have here 
five errors — one when card 3 was placed on card 4, one when 
card 4 was placed on card 3, one when card 2 was placed on card 
4, etc. The theory being that each time a wrong card is placed 
on a pile the pile takes the individuality of the new card, and 
adding any other card than the new will constitute an error. 

Count is also taken of the number of piles. Usually there 
are more errors than extra piles, but if this is not the case, each 
extra pile above the number of errors constitutes an error. 

In tabulating results I was unable to find any particular 
degree of correlation between accuracy and speed, except in in- 
dividual cases. To analyze this factor would necessitate taking 
each age as a group and evaluating the correlation. There are 
indications of such a correlation, especially in the older groups. 

In the following table seconds have been changed to frac- 
tions of a minute for convenience. 



6 6.27 

7 5.73 

8 5.29 

9 4.45 

10 4.36 

11 3.62 

12 3.79 .69 3.03 .43 3.45 .64 

13 3.45 .82 2.84 .47 3.17 .73 

14 3.13 .67 3.09 .49 3.10 .61 

In this test the girls are slower than the bo.ys except at 
the ages six, nine and fourteen. The girls' greatest variation 
comes at the point where they make their greatest gain — year 
seven. The greatest increase in speed is prior to year eleven. But 
little inci-ease (3.56 min. to 3.10 min.) is apparent from eleven 
to twelve. (See Pig. 17, upper curve.) 





TABLE XXIII. 






Card Sorting Test. 






Girls 




. V. 


Av. M. V. 


Av. 


1.23 


6.79 1.33 


6.53 


.73 


4.88 .90 


5.37 


.91 


4.50 .70 


4.86 


.62 


4.54 .95 


4.50 


.70 


3.76 .78 


4.05 


.73 


3.48 .52 


3.56 


.69 


3.03 .43 


3.45 


.82 


2.84 .47 


3.17 


.67 


3.09 .49 


3.10 



A Graduated Scale for Determiuing Mental Age 



35 





k^ 


3i^ 




"^^;^.^ 


^ 




> 16 9 10 II iz 15 la. 



TABLE XXIV. 
Average Number of Errors Made in Sorting Cards. 



Boys 6.2 

Girls 6.1 

Both 6.1 



g 


9 


10 


11 


12 


13 


14 


5.7 


5.0 


5.1 


6.0 


4.8 


5.2 


4.8 


5.4 


5.3 


4.8 


4.9 


5.0 


5.0 


4.1 


5.6 


5.2 


4.9 


5.5 


4.9 


5.1 


4.4 



In practice, and in evaluating the number of points for 
this test (see next paragraph). I add to the actual time, an addi- 
tional time of three seconds for each error. 



Evaluation of Points for the Graduated Scale. 

The assigning of weight to each of the several tests is 
necessarily an arbitrary matter. The ideal would be to give 
equal weight to the various mental processes if they could be 
labeled and tested. But that being impossible, effort was made to 
distribute the weights to the various tests in a manner which 
would facilitate, rather than hinder the task of evaluating the 
material, while at the same time distributing the points so that 
the increase from year to year would be as large as possible. 

Test I. — Allow one point for each object enumerated. 

Test II. — Allow one point for each digit. 

Test III. — Divide number of syllables by 4. (This gives 
auditory memorv for syllables the same weight as auditory mem- 
ory for digits.)' (See table XXV.) 

Test IV. — Allow two points for each figure correctly drawn. 

Test V. — Divide total number words given by 3. 

Test VI. — Niiraber of points allowed is obtained by divid- 
ing 100 by the height of the man. 

Test VII. — Multiplv points made in the seven problems by 
3. 

Test VIII. — Allow one point for each score as indicated in 
the description of this test. 

Test IX. — Divide 30 by the time taken in sorting the cards 
recorded in minutes. 



36 A Graduated Scale for Determining Mental Age 

In the summation of points boys are higher than girls 
except at year ten and the curves will probably cross soon after 
year fourteen. (See tables XXV. and XXVL) 



TABLE XXV. 
Summation of Points for Boys. 



resi 


t 6 


7 




9 


10 


11 


12 


13 


14 




3.3 


4.2 


4.3 


5.0 


5.0 


5.8 


5.6 


5.9 


6.1 


2 


4.3 


5.0 


5.4 


5.7 


5.7 




6.0 


6.1 


6.4 


3 


3.9 


4.1 


4.3 


4.6 


4.4 




5.6 


5.9 


6.1 


4 


4.0 


5.6 


7.0 


9 2 


8.6 


ll!4 


11.8 


13.6 


16.2 


5 


4.5 


4.7 


6.1 


7'.7 


7.5 




10.0 


10.3 


10.3 


6 


5.2 


5.2 


4.8 


6.3 


6.1 




10.2 


8.3 


8.7 


7 


2.1 


4.3 


5.6 


6.8 


9.2 


11^8 


12.3 


14.7 


15.7 


8 


3.0 


4.4 


6.3 


7.4 


7.1 


11.8 


13.3 


14.1 


15.3 


9 


4.6 


5.0 


5.4 


6.4 


6.4 


7.8 


7.4 


8.1 


8.9 









Summat 


lAtSLb AAVI. 

ion of Points for Girls. 






rest 


; 6 




8 


9 


10 


11 


12 


13 


14 


1 


3.3 


4.2 


4.4 


4.7 


5.0 


5.6 


5.9 


6.3 


6.6 


2 


4.5 


4.9 


5.6 


5.6 


5.5 


5.8 


6.0 


6.0 


6.3 


3 


4.0 


4.0 


4.3 






4.7 


5.5 


5.3 


5.9 


4 


3.2 


4.6 


6.2 






9.8 


10.4 


13.4 


14.0 


5 


3.9 


4.7 


5.8 






8.5 


11.6 


9.6 


11.0 


6 


4.5 


4.1 


6.2 






7.3 


5.9 


7.2 


8.5 


7 


.9 


1.2 


4.2 






11.1 


12.6 


13.6 


16.2 


8 


3.4 


4.2 


5.0 




8^3 


10.6 


11.4 


13.5 


15.4 


9 


4.2 


5.9 


6.3 


_^ 


7.5 


8.0 


9.2 


9.7 


9.1 



31.9 37.7 48.0 50.6 61.5 71.5 78.5 84.4 93.0 

For all purposes of classification, however, the two are 
combined giving the following: 



TABLE XXVII. 
Summation of Points (See Fig 18.) 

Test 6 7 8 9 10 11 12 13 14 

1 3.3 4.2 4..3 4.9 5.0 5.7 5.7 6.1 6.4 

2 4.4 4.9 5.5 5.7 5.6 5.8 6.0 6.1 6.4 

3 3.9 4.0 4.3 4.5 4.5 4.7 5.1 5.6 6.0 

4 3.6 5.2 6.6 8.0 8.8 10.6 11.2 13.6 15.0 

5 4.2 4.7 5.9 7.4 7.4 9.1 10.7 10.0 10.7 

6 4.8 4.7 5.5 5.5 5.4 6.9 7.8 7.8 8.6 

7 1.5 3.0 4.8 6.0 9.3 11.4 12.4 14.1 15.9 

8 3.2 4.3 5.6 6.8 7.7 11.2 12.4 13.8 15.4 

9 4.4 5.4 6.8 6.3 7.0 7.9 8.1 8.8 9.0 

33.3 40.0 48.8 55.1 60.6 73.3 79.4 86.9 93.4 



A Graduated Scale for Determining Mental Age 



37 



MM. 

a 

60 

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y 


■f 














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6 9 10 

Wis. IS. 



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38 A Graduated Scale for Determining Mental Age 

By use of interpolation the following table has been con- 
structed from the norms given above and serves the purpose of 
quickly estimating the ages to a tenth of a year. 









Table 


XXVIII. 








No. 


Ment. 


No. 


Ment. 


No. 


Ment. 


No. 


Ment, 


Points 


Age 


Points 


Age 


Points 


Age 


Points 


Age 


33.3 


6.0 


48.4 


8.0 


60.6 


10.0 


79.4 


12.0 


34.0 


6.1 


49.1 


8.1 


61.9 


10.1 


80.1 


12.1 


34.7 


e.2 


49.7 


8.2 


63.1 


10.2 


80.7 


12.2 


35.4 


6.3 


50.4 


8.3 


64.4 


10.3 


81.4 


12.3 


36.1 


6.4 


51.1 


8.4 


65.7 


10.4 


82.0 


12.4 


36.9 


6.5 


51.8 


8.5 


67.0 


10.5 


82.7 


12.5 


37.6 


6.6 


52.4 


8.6 


68.2 


10.6 


83.3 


12.6 




6.7 


53.1 


8.7 


69.5 


10.7 


84.0 


12.7 


ssio 


6.8 


53.8 


8.8 


70.8 


10.8 


84.6 


12.8 


39.7 


6.9 


54.4 


8.9 


72.0 


10.9 


85.3 


12.9 


40.4 


7.0 


55.1 


9.0 


73.3 


11.0 


85.9 


13.0 


41.2 


7.1 


55.7 


9.1 


73.9 


11.1 


86.7 


13.1 


42.0 


7.2 


56.2 


9.2 


74.5 


11.2 


87.4 


13.2 


42.8 


7.3 


56.8 


9.3 


75.1 


11.3 


88.2 


13.3 


43.6 


7.4 


57.3 


9.4 


75.7 


11.4 


88.9 


13.4 


44.4 


7.5 


57.9 


9.5 


76.4 


11.5 


89.7 


13.5 


45.2 


7.6 


58.4 


9.6 


77.0 


11.6 


90.4 


13.6 


46.0 


7.7 


59.0 


9.7 


77.6 


11.7 


91.2 


13.7 


46.8 


7.8 


59.5 


9.8 


78.2 


11.8 


91.9 


13.8 


47.6 


7.9 


60.1 


9.9 


78.8 


11.9 


92.7 
93.4 


13.9 
14.0 



m 

In illustration of the use of the scale I shall add a few 
actual eases, selected at random from among those which were 
given for special reasons. 

(1) R. W., a girl, age 10 years, 1 month, seven days; 
5A grade. Points made for each test are, respectively, .5.7, 5.5, 
11, 8.6, 7.1, 15, 10, 8.1, a total of 77.3. Referring to table XXVII., 
the mental age is found to be 11.65 years, showing an accelera- 
tion of 1.5 years. 

(2) J. B., a boy, age 13 years, 2 months, 17 days; 7A 
grade. Points made, 5, 5, 5, 23, "8.3, 4.2, 15, 12, 9.2, total 86.7. 
Mental age 13.1, which is identical with the chronological age. 

(3) R. C, a girl, age 11 years, 4 months, 16 days; 3B 
grade. Points made 3, 6, 5, 4, 7.6, 7, 1.5, 9, 4.8, total 47.9. Mental 
age, 7.9, which is 3.4 years below her chronological age. 

(4) C. G., a boy, age 10 years, 1 month : 4A grade. Points 
made, 5, 7, 6, 17, 6.6, 8.7, 18, 11, 7.5, a total of 86.8. Mental age 
13.1, which is 3 years in advance of his chronological age. 

The list could be extended indefinitely from the data at 
hand, but no attempt has been made to summarize the work 
with these special cases, hence I submit merely the above in 
illustration of the use of the scale. 

Conclusion. 

After using the scale in testing between five and six hundred 
children I have become firmly convinced of its applicability as 
an instrument for "first aid" purposes. Indeed, its results are 
sufficient to classify satisfactorily the majority of cases. 
Throughout the work. T repeatedly compared notes with the 



A Graduated Scale for Determining Mental Age 39 

teacher and principal, and practically without exception, found 
that my estimate of the child corresponded with that of the iri- 
strnctor. At each school which I visited I was requested to 
examine special cases, with the result that the scale was thor- 
oughly tried out. Wlien examining children at the request of 
the teacher or principal I made it a rule to take the case as an 
"unknown."' With very few exceptions my findings were cor- 
roborated by the facts as shown by class standing and the esti- 
mate of the teacher. In many cases I have pointed out individ- 
ual peculiarities which had passed unnoticed, but which were at 
once recognized when the teacher's attention was directed to- 
ward them. A glaring example came to light one day while I 
was testing children for special promotion. A boy of twelve 
in the sixth grade had been recommended as a candidate but, 
owing to his retiring disposition, his teachers were not convinced 
that he would be able to carrj' the advanced work. I found 
that he was mentally about four years in advance of his age — 
entirely beyond the range of my scale — and capable of carrying 
high school work. Even his mother was forced to admit that, 

even though L was not considered precocious, she always 

appealed to him as a court of last resort, when special informa- 
tion was wanted. As a result of my findings he was advanced 
one grade and placed in the special preparatory school. 

This confidence in the scale prompts me to make the state- 
ment that it can be used by teachers and supervisors with grati- 
fring results. With its application one can ascertain more in 
thirty minutes concerning the actual mental condition of the 
child than is ordinarily possible from two years of regular 
school work. Moreover its compactness and simplicity of opera- 
tion commend it especially to teachers who lack a complete 
training in experimental pedagog;\'. 

There is no question but that such a measuring instrument 
may be used greatly to increase the efficiency of any school 
system. There should be several scales available but all of a 
type which would commend their iise to the rank and file of the 
teaching profession. Only by a conscientious effort in classi- 
fication will the schools of America be able to reach the standard 
which the public has a right to demand of them — the standard 
which gives each individual child the most efficient education of 
which he is capable. 

Bibliography,* 

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3. Binet, A. — "L 'etude experimentelle de Intelligence." 
Paris. 1902. 

4. Binet, A., and Simon. Th, — "A Method of Measuring the 



*No attempt is here made to compile a complete bibliography. 
This has been ably done by Samuel C. Kohs in recent numbers of the 
Journal of Educational Psychology, and is now available in book 
form." 



40 A Graduated Scale for Determining Mental Age 

Development of the Intelligence of Young Children." Trans. 
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8. "Ueber eine neue Methods zur Prufung 

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26. — "Educational Psychology." Teach- 
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A Graduated Scale for Determining Mental Age 41 

27. Wallin, J. E. W.— "A Critique of the Binet-Simon 
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